ON the night of June 14, 1770, the great French astronomer Messier first saw the captive comet. It then appeared as a small patch of haze against the cloudless sky, but it rapidly grew larger and more brilliant, until, on July 2d, when it passed nearer to the earth than any other known comet, it was as bright as the North Star, and its diameter was twice that of the full moon. From that moment its brilliancy faded, it grew fainter and fainter, and was seen for the last time on October 2d.

While this comet of 1770 is one of the most famous in the annals of astronomy, it owes its celebrity not to the spectacular effects it produced, for it was not one of those magnificent objects that stretch across the heavens, exciting the wonder and admiration of the intelligent, the fear and dread of the ignorant. Its fame is due to its mathematical history, to the path it was then traveling, and to the path it has since traveled. Only twenty years had elapsed since Halley had made his great discovery of the existence of periodic comets, and this comet of 1770 was shown by Lexell to belong to this interesting class of bodies, to be then revolving around the sun in an ellipse of five and a half years. To the conclusions of Lexell it was at once objected by other mathematicians that if this comet revolved about the sun in an ellipse, like the planets, it should have been seen six years before, and again, six years before that; at least, some record of its former appearances ought certainly to be found. As there were no such records, as it could be shown that there was no comet that had appeared regularly every five and a half or six years, Lexell's opinions were for the moment discredited. However, he soon conclusively proved that he was right, that the comet was moving at the moment in an ellipse such as he had described, but that it had not always traveled in that same path. He showed that in 1767, or only three years previously, the comet had passed very close to the giant planet Jupiter, and that then its path had been greatly altered, so completely changed, indeed, that never before had it passed near enough to the earth to be seen. He also predicted a second close approach of these two bodies in 1779, and said that this circumstance might prevent the reappearance of the comet after that date. This prediction of Lexell's was fulfilled, for the comet was never again seen, unless it prove that the comet discovered by Brooks on July G, 1889, is the lost body.

On that summer evening, at Geneva, N. Y., Brooks discovered a faint telescopic comet, since known as comet d and V, 1889. As this body never became visible to the naked eye, it received but passing notice from the daily newspapers; even astronomers, at first, thought very little of it, as the discovery of a new comet is now a matter of almost monthly occurrence. It was not long, however, before this body began to attract the attention of the scientific world, and it was soon recognized as a permanent member of the solar system; and now, through the researches of Dr. Chandler and others, it has become the most famous comet of this century. It has been identified with the lost comet of Lexell, which disappeared one hundred and twenty years ago.

Upon what grounds do we base this conclusion? A comet was seen for but a few months during the summer of 1770, another one is observed during the summer and fall of 1889, and it is asserted that these two bodies are identical. There are no physical means by which they can be identified, for comets have no permanent characteristics which, when once seen, can always be recognized. Indeed, to all appearances, these two bodies were utterly unlike: the comet of 1770 was large and bright, with a well-marked tail; while the comet of 1889 was hardly visible even with powerful telescopes, and then appeared but as a small patch of haze against the dark sky. If, then, we rely on similarity of appearance to establish the identity of these two comets, we should fail to do so, and would be forced to conclude that they are not the same. But by a study of the movements of the two, especially of the latter, it can be shown that they must have occupied, at one time, the same position in space—their identity is then self-evident.

At present the comet is moving in a small ellipse of about seven years' period. This path is shown in the diagram. The smallest circle represents the annual orbit of the earth around the sun. Just outside of this circle is a heavily drawn ellipse with one of its foci at the sun. This is the present orbit of comet V, and on it are marked three positions of this interesting body. The first, July 6, 1889, marks its position on the night of discovery; the second, September 30th, at its perihelion passage, or nearest approach to the sun; the third, that of December, 1890, the position it occupied when last seen. For months before this last date, however, the comet could only be seen by means of the great thirty-six-inch Lick telescope. Between the two extreme positions above mentioned, there are scattered along the curve some two hundred and fifty other observations; and on this small part of the comet's path rest all the conclusions as to its movements for over a hundred years.

The first step in the problem was to deduce from these observed positions the orbit of the comet, or the ellipse shown in the diagram. This curve should be clearly understood—it is not the actual path of the comet through the heavens, but that path which it would describe if the comet and sun were the only two bodies in existence. The earth, Jupiter, all the planets are, in fact, pulling and hauling at the unfortunate body: first one drags it a little one way, then another pulls it in a different direction. The real path of the comet about the sun is, then, a very complicated, wavy sort of a curve, which, as a rule, does not depart very much from the ellipse above figured.

Now, while mathematicians have succeeded in completely solving the problem of two bodies, yet, up to the present day, that of three or more bodies is still unsolved. If the sun and comet were the only two bodies in the universe, then could a mathematician, after a few moments' calculation, predict exactly where each would be a thousand years hence; could tell where they were ten thousand years ago. But as soon as there is introduced into such a simple system the earth, Jupiter, and the other planets, our mathematics fails to give a complete solution. All that can be done is to trace the course of the comet step by step, day by day, almost. We know its position to-day, and we can accurately calculate the direction and the amount of the pull of each planet; hence, we can find where it will be to-morrow, and, by repeating the process, where it will be the next day, and the next. Of course, this is a very laborious process; the calculation of the pull of a single planet requires the writing and the combination of one hundred and fifty numbers of six figures each. But, fortunately, the sun is over a thousand times as strong as the great planet Jupiter, and over three hundred thousand times as strong as the earth; so that, unless the comet approach very near to one of the larger planets, it will never deviate much from its simple orbit around the sun. The steps in our computation may be, therefore, lengthened. The ordinary length of step in such work is forty days; and, in a first computation, the pulls of the smaller politicians—as the earth, Venus, and Mars—can be neglected beside the very strong ones of Jupiter and Saturn.

As we wished to trace the history of comet V, we started with the earliest observed position, that of July 6, 1889, and we began by taking steps of forty days each. Thus the path the comet had traveled was slowly traced backward, and it was found to approach nearer and nearer to Jupiter. Proceeding backward thus over a period of two years, we find that in March, 1887, the pull of Jupiter was so strong that, in order to keep the work at all accurate, we were obliged to shorten the steps to ten days. Continuing thus, the pull of Jupiter grew stronger and stronger, until, in October, 1886, it was actually greater than that of the sun, and a change of method had to be used in order to trace the path beyond that point, and with this change in methods appears the interesting mathematical part of the problem.

It is now perfectly well known to every schoolboy that the sun is the center and ruler of the solar system; that the earth and other planets revolve about it in great ellipses. This simple fact

New and Old Orbits of Comet V, 1889.

was not recognized, however, until nearly the middle of the sixteenth century. For thousands of years previously, astronomers as well as priests, the educated and the ignorant, had thought that the earth was the center of the universe; that the sun, the planets, and the countless stars revolved around and were accessory to this little abode of man.

Ptolemy, the greatest astronomer of the ancients, put this false theory on a strict mathematical basis. By means of his cumbersome system of epicycles he could roughly compute the positions of the planets at any time, could foretell the time of rising and setting of the moon, and predict eclipses. But, while the Ptolemaic system is false, while it does not agree with what we now know to be the true system of the heavens, yet it is mathematically possible. In discussing the various positions and motions of the planets, it would be perfectly possible to consider the earth as the fixed point around which they move; we could thus arrive at correct results, but the processes would be infinitely long and complicated. And yet a modification of this antiquated method was the only means of tracing further the path of this interesting comet, for the pull of Jupiter became now so strong that, in our backward path, we would have had to take steps, not of a few days, not of a few hours, but of twenty or thirty minutes at a time. The task would have been endless.

Jupiter was now the ruler of the comet's destiny, the sun a mere disturbing element, so that it became simpler to give Jupiter its just position as ruler at the center of the comet's motion.

Jupiter was made the momentary center of the universe; comet, sun, earth, and planets were all considered as revolving around this monster planet. The change of the center of motion from the sun to Jupiter was easily effected, and the resulting orbit of the comet about Jupiter was found to be a hyperbola, an open curve. And now, just as before, this curve is merely the path the comet would have described about Jupiter if it and the planet were the only two bodies in existence; the long-suffering comet is still pulled and hauled at by various bodies, notably the sun, and step by step its path had to be traced out. At first, steps of ten days each were found to be sufficiently accurate, but as the comet approached closer and closer to Jupiter it began to move faster and faster, and consequently the length of the steps had to be shortened to four days each. After the comet had passed Jupiter the length of the steps was gradually lengthened again.

The remarkable character of this appulse should be clearly understood. The comet passed the center of Jupiter in 1886, July 19th, at no greater distance than two and one third radii of that planet. It must then have passed the surface of Jupiter at a distance of only one and one third radii—that is, the center of the comet was only about sixty thousand miles from the surface of the planet. It is not at all improbable that parts of the diffused mass of the comet swept over the surface of Jupiter itself, and that we had here a true collision between the two bodies. The comet struck the planet a glancing blow, as it were. As is usual in all collisions, the weaker body suffered: the comet was broken into three parts, while Jupiter was unharmed.

When the comet had passed far enough away from Jupiter, so that the sun had regained its supremacy, the motion was again referred to the sun as fixed point, and the tedious process of tracing the comet's history continued, step by step. Tracing thus backward the path of this minute body, we find that it leads to the spot where Lexell's comet disappeared in 1779. Either two comets can occupy the same space at the same time, or the comets of 1770 and 1889 are one and the same.

We have thus seen something of the laborious process by which, starting with a few observed positions of a body in 1889, we can trace the path it has traveled for one hundred and seven years; how we can show its identity with a comet seen in 1770. Of the path itself but little has yet been said. It is interesting. And as it is always easier to trace a succession of events in the order in which they occur than it is to reverse the order of time, we will start with the first recorded public appearance of the comet, in 1770, and give a brief sketch of its erratic course through the heavens since that moment—though, remember, this path was discovered by tracing the body backward along its course.

Look again at the diagram. In the summer of 1770 the comet was seen moving along the small dotted curve in the region very close to the smallest circle in the diagram, which represents the orbit of the earth. It disappeared from view and passed outward along this dotted curve, making one complete revolution, returning in 1775 to the point where it was first seen. During these few years the earth had also been traveling its yearly path around the sun, and it so happened that in this latter year (1775) the earth had moved into a different position in its orbit, so that the sun was directly between it and the comet. The comet was therefore not then seen. Onward went the comet along this dotted path, until, in 1779, it had reached the outermost point, when it encountered Jupiter. The effects of this appulse were very marked as regards the comet: it was pushed completely out of its path and set moving in an immense ellipse, the one that extends far out to the left in the diagram. From five and a half years its period had been changed to about thirty-four years. In this large path this captive body moved without any extraordinary incident for sixty-seven years, or until 1846. During this time it had traveled twice around the curve, and it was fairly started on its third trip, when Saturn took a hand in the game and altered its path considerably, extending the ellipse to one of forty-seven years period. On it went, but it was never allowed to complete even one revolution in this last ellipse, for in 1886 it collided with Jupiter, as has been already described, and its path was changed to the small ellipse in which the justly famous comet is now moving, and in which it will continue to move for a number of years to come.